A Multifractional Process with Random Exponent (MPRE) is used to model the dynamics of log-prices in a financial market. Under this assumption, we show that the Hurst-Hölder exponent of the MPRE follows the fractional Ornstein-Uhlenbeck process which in the Fractional Stochastic Volatility Model of Comte and Renault (1998) describes the dynamics of the log-volatility. We provide evidence that several biases of the estimation procedures can generate artificial rough volatility in surrogated as well as real financial data.
Nonlinear biases in the roughness of a Fractional Stochastic Regularity Model / Angelini, Daniele; Bianchi, Sergio. - In: CHAOS, SOLITONS & FRACTALS. - ISSN 1873-2887. - 172(2023).
Nonlinear biases in the roughness of a Fractional Stochastic Regularity Model
Angelini Daniele;Sergio Bianchi
2023
Abstract
A Multifractional Process with Random Exponent (MPRE) is used to model the dynamics of log-prices in a financial market. Under this assumption, we show that the Hurst-Hölder exponent of the MPRE follows the fractional Ornstein-Uhlenbeck process which in the Fractional Stochastic Volatility Model of Comte and Renault (1998) describes the dynamics of the log-volatility. We provide evidence that several biases of the estimation procedures can generate artificial rough volatility in surrogated as well as real financial data.| File | Dimensione | Formato | |
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